What is more pollutive per person, to cross the Atlantic Ocean by a tanker ship, a cruise ship, or an airplane?

First we must differentiate between the two systems Liner Service & Tramp Service

  Liner Service – is a service that operates within a schedule and has a fixed port rotation with published dates of calls at the advertised ports.. A liner service generally fulfills the schedule unless in cases where a call at one of the ports has been unduly delayed due to natural or man-mad causes..

Example : The UK/NWC continent service of MSC which has a fixed weekly schedule calling the South African ports of Durban, Cape Town and Port Elizabeth and carrying cargo to the UK/NWC ports of Felixstowe, Antwerp, Hamburg, Le Havre and Rotterdam

A Tramp Service or tramper on the other hand is a ship that has no fixed routing or itinerary or schedule and is available at short notice (or fixture) to load any cargo from any port to any port..

Example : A ship that arrives at Durban from Korea to discharge cargo might carry some other cargo from Durban to the Oakland in the West Coast of USA which in an entirely different direction.. From Oakland say for example it could carry some cargo and go to Bremerhaven..

so I prefer  the tanker ship also full of cargo or just jammed full of people? Using fuel costs as a proxy for carbon emissions, and shipping costs as a proxy for fuel costs, I'd vote for the cargo ship, at least per pound of passenger.